document.write( "Question 153291: One third of the result of twice a certain number is added to one. The resulting expression is equivalent to one quarter of twice the certain number. Write an equation and solve. \n" ); document.write( "

Algebra.Com's Answer #112815 by orca(409) $\"\"$ $\"About$

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Let x be the number.
\n" ); document.write( "One third of the result of twice a certain number plus one can be expressed as:
\n" ); document.write( " $\"%281%2F3%29%2A2x%2B1%29\"$
\n" ); document.write( "One quarter of twice the certain number can be expressed as:
\n" ); document.write( " $\"%281%2F4%29%2A2x\"$
\n" ); document.write( "According to the given information, these two expressions are the same. So we have:
\n" ); document.write( " $\"%281%2F3%29%2A2x%2B1=%281%2F4%29%2A2x\"$
\n" ); document.write( "Solving for x, we have
\n" ); document.write( " $\"2x%2F3%2B1=x%2F2\"$
\n" ); document.write( " $\"6%2A%282x%2F3%2B1%29=6%28x%2F2%29\"$ (multiply both sides by 6)
\n" ); document.write( " $\"4x%2B6=3x\"$
\n" ); document.write( " $\"x=-6\"$
\n" ); document.write( "So the number is -6.
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